Properties

Label 7098.2.a.ct.1.1
Level $7098$
Weight $2$
Character 7098.1
Self dual yes
Analytic conductor $56.678$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7098.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(56.6778153547\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.48406561.1
Defining polynomial: \(x^{6} - 3 x^{5} - 17 x^{4} + 39 x^{3} + 111 x^{2} - 131 x - 281\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.41496\) of defining polynomial
Character \(\chi\) \(=\) 7098.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.41496 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.41496 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.41496 q^{10} +3.24698 q^{11} +1.00000 q^{12} +1.00000 q^{14} -2.41496 q^{15} +1.00000 q^{16} +1.80194 q^{17} +1.00000 q^{18} -2.73858 q^{19} -2.41496 q^{20} +1.00000 q^{21} +3.24698 q^{22} -6.58012 q^{23} +1.00000 q^{24} +0.832022 q^{25} +1.00000 q^{27} +1.00000 q^{28} +6.22322 q^{29} -2.41496 q^{30} +2.72294 q^{31} +1.00000 q^{32} +3.24698 q^{33} +1.80194 q^{34} -2.41496 q^{35} +1.00000 q^{36} +8.93878 q^{37} -2.73858 q^{38} -2.41496 q^{40} +9.15862 q^{41} +1.00000 q^{42} -3.95322 q^{43} +3.24698 q^{44} -2.41496 q^{45} -6.58012 q^{46} +9.77289 q^{47} +1.00000 q^{48} +1.00000 q^{49} +0.832022 q^{50} +1.80194 q^{51} -10.3747 q^{53} +1.00000 q^{54} -7.84132 q^{55} +1.00000 q^{56} -2.73858 q^{57} +6.22322 q^{58} -4.50007 q^{59} -2.41496 q^{60} +6.94297 q^{61} +2.72294 q^{62} +1.00000 q^{63} +1.00000 q^{64} +3.24698 q^{66} -2.54486 q^{67} +1.80194 q^{68} -6.58012 q^{69} -2.41496 q^{70} -1.50961 q^{71} +1.00000 q^{72} -0.786291 q^{73} +8.93878 q^{74} +0.832022 q^{75} -2.73858 q^{76} +3.24698 q^{77} -2.41753 q^{79} -2.41496 q^{80} +1.00000 q^{81} +9.15862 q^{82} -3.51468 q^{83} +1.00000 q^{84} -4.35160 q^{85} -3.95322 q^{86} +6.22322 q^{87} +3.24698 q^{88} +10.9361 q^{89} -2.41496 q^{90} -6.58012 q^{92} +2.72294 q^{93} +9.77289 q^{94} +6.61356 q^{95} +1.00000 q^{96} +12.2904 q^{97} +1.00000 q^{98} +3.24698 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 6q^{2} + 6q^{3} + 6q^{4} + 3q^{5} + 6q^{6} + 6q^{7} + 6q^{8} + 6q^{9} + O(q^{10}) \) \( 6q + 6q^{2} + 6q^{3} + 6q^{4} + 3q^{5} + 6q^{6} + 6q^{7} + 6q^{8} + 6q^{9} + 3q^{10} + 10q^{11} + 6q^{12} + 6q^{14} + 3q^{15} + 6q^{16} + 2q^{17} + 6q^{18} + 2q^{19} + 3q^{20} + 6q^{21} + 10q^{22} + 4q^{23} + 6q^{24} + 13q^{25} + 6q^{27} + 6q^{28} + 2q^{29} + 3q^{30} + 9q^{31} + 6q^{32} + 10q^{33} + 2q^{34} + 3q^{35} + 6q^{36} + 7q^{37} + 2q^{38} + 3q^{40} + 11q^{41} + 6q^{42} - 5q^{43} + 10q^{44} + 3q^{45} + 4q^{46} + 5q^{47} + 6q^{48} + 6q^{49} + 13q^{50} + 2q^{51} - 6q^{53} + 6q^{54} + 5q^{55} + 6q^{56} + 2q^{57} + 2q^{58} + 28q^{59} + 3q^{60} + 23q^{61} + 9q^{62} + 6q^{63} + 6q^{64} + 10q^{66} - 10q^{67} + 2q^{68} + 4q^{69} + 3q^{70} + 21q^{71} + 6q^{72} - 7q^{73} + 7q^{74} + 13q^{75} + 2q^{76} + 10q^{77} - 14q^{79} + 3q^{80} + 6q^{81} + 11q^{82} + 17q^{83} + 6q^{84} + q^{85} - 5q^{86} + 2q^{87} + 10q^{88} + 17q^{89} + 3q^{90} + 4q^{92} + 9q^{93} + 5q^{94} - 22q^{95} + 6q^{96} + 6q^{98} + 10q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) −2.41496 −1.08000 −0.540001 0.841664i \(-0.681576\pi\)
−0.540001 + 0.841664i \(0.681576\pi\)
\(6\) 1.00000 0.408248
\(7\) 1.00000 0.377964
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) −2.41496 −0.763677
\(11\) 3.24698 0.979001 0.489501 0.872003i \(-0.337179\pi\)
0.489501 + 0.872003i \(0.337179\pi\)
\(12\) 1.00000 0.288675
\(13\) 0 0
\(14\) 1.00000 0.267261
\(15\) −2.41496 −0.623539
\(16\) 1.00000 0.250000
\(17\) 1.80194 0.437034 0.218517 0.975833i \(-0.429878\pi\)
0.218517 + 0.975833i \(0.429878\pi\)
\(18\) 1.00000 0.235702
\(19\) −2.73858 −0.628274 −0.314137 0.949378i \(-0.601715\pi\)
−0.314137 + 0.949378i \(0.601715\pi\)
\(20\) −2.41496 −0.540001
\(21\) 1.00000 0.218218
\(22\) 3.24698 0.692258
\(23\) −6.58012 −1.37205 −0.686025 0.727578i \(-0.740646\pi\)
−0.686025 + 0.727578i \(0.740646\pi\)
\(24\) 1.00000 0.204124
\(25\) 0.832022 0.166404
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 1.00000 0.188982
\(29\) 6.22322 1.15562 0.577812 0.816170i \(-0.303907\pi\)
0.577812 + 0.816170i \(0.303907\pi\)
\(30\) −2.41496 −0.440909
\(31\) 2.72294 0.489054 0.244527 0.969643i \(-0.421367\pi\)
0.244527 + 0.969643i \(0.421367\pi\)
\(32\) 1.00000 0.176777
\(33\) 3.24698 0.565227
\(34\) 1.80194 0.309030
\(35\) −2.41496 −0.408202
\(36\) 1.00000 0.166667
\(37\) 8.93878 1.46953 0.734764 0.678323i \(-0.237293\pi\)
0.734764 + 0.678323i \(0.237293\pi\)
\(38\) −2.73858 −0.444257
\(39\) 0 0
\(40\) −2.41496 −0.381838
\(41\) 9.15862 1.43034 0.715168 0.698953i \(-0.246350\pi\)
0.715168 + 0.698953i \(0.246350\pi\)
\(42\) 1.00000 0.154303
\(43\) −3.95322 −0.602861 −0.301430 0.953488i \(-0.597464\pi\)
−0.301430 + 0.953488i \(0.597464\pi\)
\(44\) 3.24698 0.489501
\(45\) −2.41496 −0.360001
\(46\) −6.58012 −0.970186
\(47\) 9.77289 1.42552 0.712761 0.701407i \(-0.247444\pi\)
0.712761 + 0.701407i \(0.247444\pi\)
\(48\) 1.00000 0.144338
\(49\) 1.00000 0.142857
\(50\) 0.832022 0.117666
\(51\) 1.80194 0.252322
\(52\) 0 0
\(53\) −10.3747 −1.42507 −0.712536 0.701636i \(-0.752453\pi\)
−0.712536 + 0.701636i \(0.752453\pi\)
\(54\) 1.00000 0.136083
\(55\) −7.84132 −1.05732
\(56\) 1.00000 0.133631
\(57\) −2.73858 −0.362734
\(58\) 6.22322 0.817149
\(59\) −4.50007 −0.585859 −0.292930 0.956134i \(-0.594630\pi\)
−0.292930 + 0.956134i \(0.594630\pi\)
\(60\) −2.41496 −0.311770
\(61\) 6.94297 0.888957 0.444478 0.895790i \(-0.353389\pi\)
0.444478 + 0.895790i \(0.353389\pi\)
\(62\) 2.72294 0.345813
\(63\) 1.00000 0.125988
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 3.24698 0.399676
\(67\) −2.54486 −0.310904 −0.155452 0.987843i \(-0.549683\pi\)
−0.155452 + 0.987843i \(0.549683\pi\)
\(68\) 1.80194 0.218517
\(69\) −6.58012 −0.792153
\(70\) −2.41496 −0.288643
\(71\) −1.50961 −0.179157 −0.0895787 0.995980i \(-0.528552\pi\)
−0.0895787 + 0.995980i \(0.528552\pi\)
\(72\) 1.00000 0.117851
\(73\) −0.786291 −0.0920283 −0.0460142 0.998941i \(-0.514652\pi\)
−0.0460142 + 0.998941i \(0.514652\pi\)
\(74\) 8.93878 1.03911
\(75\) 0.832022 0.0960736
\(76\) −2.73858 −0.314137
\(77\) 3.24698 0.370028
\(78\) 0 0
\(79\) −2.41753 −0.271993 −0.135997 0.990709i \(-0.543424\pi\)
−0.135997 + 0.990709i \(0.543424\pi\)
\(80\) −2.41496 −0.270001
\(81\) 1.00000 0.111111
\(82\) 9.15862 1.01140
\(83\) −3.51468 −0.385786 −0.192893 0.981220i \(-0.561787\pi\)
−0.192893 + 0.981220i \(0.561787\pi\)
\(84\) 1.00000 0.109109
\(85\) −4.35160 −0.471998
\(86\) −3.95322 −0.426287
\(87\) 6.22322 0.667200
\(88\) 3.24698 0.346129
\(89\) 10.9361 1.15922 0.579610 0.814894i \(-0.303205\pi\)
0.579610 + 0.814894i \(0.303205\pi\)
\(90\) −2.41496 −0.254559
\(91\) 0 0
\(92\) −6.58012 −0.686025
\(93\) 2.72294 0.282355
\(94\) 9.77289 1.00800
\(95\) 6.61356 0.678537
\(96\) 1.00000 0.102062
\(97\) 12.2904 1.24790 0.623950 0.781464i \(-0.285527\pi\)
0.623950 + 0.781464i \(0.285527\pi\)
\(98\) 1.00000 0.101015
\(99\) 3.24698 0.326334
\(100\) 0.832022 0.0832022
\(101\) 15.5746 1.54973 0.774866 0.632126i \(-0.217817\pi\)
0.774866 + 0.632126i \(0.217817\pi\)
\(102\) 1.80194 0.178418
\(103\) 3.71813 0.366358 0.183179 0.983080i \(-0.441361\pi\)
0.183179 + 0.983080i \(0.441361\pi\)
\(104\) 0 0
\(105\) −2.41496 −0.235676
\(106\) −10.3747 −1.00768
\(107\) −0.125781 −0.0121597 −0.00607983 0.999982i \(-0.501935\pi\)
−0.00607983 + 0.999982i \(0.501935\pi\)
\(108\) 1.00000 0.0962250
\(109\) 3.84276 0.368070 0.184035 0.982920i \(-0.441084\pi\)
0.184035 + 0.982920i \(0.441084\pi\)
\(110\) −7.84132 −0.747640
\(111\) 8.93878 0.848432
\(112\) 1.00000 0.0944911
\(113\) 12.7648 1.20082 0.600408 0.799694i \(-0.295005\pi\)
0.600408 + 0.799694i \(0.295005\pi\)
\(114\) −2.73858 −0.256492
\(115\) 15.8907 1.48182
\(116\) 6.22322 0.577812
\(117\) 0 0
\(118\) −4.50007 −0.414265
\(119\) 1.80194 0.165183
\(120\) −2.41496 −0.220454
\(121\) −0.457123 −0.0415567
\(122\) 6.94297 0.628587
\(123\) 9.15862 0.825805
\(124\) 2.72294 0.244527
\(125\) 10.0655 0.900285
\(126\) 1.00000 0.0890871
\(127\) −11.7970 −1.04682 −0.523408 0.852082i \(-0.675340\pi\)
−0.523408 + 0.852082i \(0.675340\pi\)
\(128\) 1.00000 0.0883883
\(129\) −3.95322 −0.348062
\(130\) 0 0
\(131\) −16.5193 −1.44330 −0.721649 0.692259i \(-0.756615\pi\)
−0.721649 + 0.692259i \(0.756615\pi\)
\(132\) 3.24698 0.282613
\(133\) −2.73858 −0.237465
\(134\) −2.54486 −0.219843
\(135\) −2.41496 −0.207846
\(136\) 1.80194 0.154515
\(137\) 11.5650 0.988068 0.494034 0.869443i \(-0.335522\pi\)
0.494034 + 0.869443i \(0.335522\pi\)
\(138\) −6.58012 −0.560137
\(139\) −2.63433 −0.223441 −0.111720 0.993740i \(-0.535636\pi\)
−0.111720 + 0.993740i \(0.535636\pi\)
\(140\) −2.41496 −0.204101
\(141\) 9.77289 0.823026
\(142\) −1.50961 −0.126683
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −15.0288 −1.24808
\(146\) −0.786291 −0.0650739
\(147\) 1.00000 0.0824786
\(148\) 8.93878 0.734764
\(149\) −19.3553 −1.58565 −0.792825 0.609450i \(-0.791391\pi\)
−0.792825 + 0.609450i \(0.791391\pi\)
\(150\) 0.832022 0.0679343
\(151\) 9.50760 0.773717 0.386859 0.922139i \(-0.373560\pi\)
0.386859 + 0.922139i \(0.373560\pi\)
\(152\) −2.73858 −0.222128
\(153\) 1.80194 0.145678
\(154\) 3.24698 0.261649
\(155\) −6.57578 −0.528179
\(156\) 0 0
\(157\) 2.70530 0.215907 0.107953 0.994156i \(-0.465570\pi\)
0.107953 + 0.994156i \(0.465570\pi\)
\(158\) −2.41753 −0.192328
\(159\) −10.3747 −0.822766
\(160\) −2.41496 −0.190919
\(161\) −6.58012 −0.518586
\(162\) 1.00000 0.0785674
\(163\) −6.79361 −0.532117 −0.266058 0.963957i \(-0.585721\pi\)
−0.266058 + 0.963957i \(0.585721\pi\)
\(164\) 9.15862 0.715168
\(165\) −7.84132 −0.610446
\(166\) −3.51468 −0.272792
\(167\) 17.9654 1.39020 0.695101 0.718912i \(-0.255360\pi\)
0.695101 + 0.718912i \(0.255360\pi\)
\(168\) 1.00000 0.0771517
\(169\) 0 0
\(170\) −4.35160 −0.333753
\(171\) −2.73858 −0.209425
\(172\) −3.95322 −0.301430
\(173\) −7.21332 −0.548418 −0.274209 0.961670i \(-0.588416\pi\)
−0.274209 + 0.961670i \(0.588416\pi\)
\(174\) 6.22322 0.471781
\(175\) 0.832022 0.0628949
\(176\) 3.24698 0.244750
\(177\) −4.50007 −0.338246
\(178\) 10.9361 0.819693
\(179\) 3.27893 0.245079 0.122539 0.992464i \(-0.460896\pi\)
0.122539 + 0.992464i \(0.460896\pi\)
\(180\) −2.41496 −0.180000
\(181\) 21.0091 1.56160 0.780798 0.624783i \(-0.214813\pi\)
0.780798 + 0.624783i \(0.214813\pi\)
\(182\) 0 0
\(183\) 6.94297 0.513239
\(184\) −6.58012 −0.485093
\(185\) −21.5868 −1.58709
\(186\) 2.72294 0.199655
\(187\) 5.85086 0.427857
\(188\) 9.77289 0.712761
\(189\) 1.00000 0.0727393
\(190\) 6.61356 0.479798
\(191\) −6.15290 −0.445208 −0.222604 0.974909i \(-0.571456\pi\)
−0.222604 + 0.974909i \(0.571456\pi\)
\(192\) 1.00000 0.0721688
\(193\) −18.6232 −1.34053 −0.670265 0.742122i \(-0.733819\pi\)
−0.670265 + 0.742122i \(0.733819\pi\)
\(194\) 12.2904 0.882398
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 16.8553 1.20089 0.600443 0.799667i \(-0.294991\pi\)
0.600443 + 0.799667i \(0.294991\pi\)
\(198\) 3.24698 0.230753
\(199\) 12.3376 0.874589 0.437295 0.899318i \(-0.355937\pi\)
0.437295 + 0.899318i \(0.355937\pi\)
\(200\) 0.832022 0.0588328
\(201\) −2.54486 −0.179501
\(202\) 15.5746 1.09583
\(203\) 6.22322 0.436785
\(204\) 1.80194 0.126161
\(205\) −22.1177 −1.54477
\(206\) 3.71813 0.259055
\(207\) −6.58012 −0.457350
\(208\) 0 0
\(209\) −8.89213 −0.615081
\(210\) −2.41496 −0.166648
\(211\) −15.6160 −1.07505 −0.537525 0.843248i \(-0.680641\pi\)
−0.537525 + 0.843248i \(0.680641\pi\)
\(212\) −10.3747 −0.712536
\(213\) −1.50961 −0.103437
\(214\) −0.125781 −0.00859818
\(215\) 9.54686 0.651091
\(216\) 1.00000 0.0680414
\(217\) 2.72294 0.184845
\(218\) 3.84276 0.260264
\(219\) −0.786291 −0.0531326
\(220\) −7.84132 −0.528662
\(221\) 0 0
\(222\) 8.93878 0.599932
\(223\) 5.53203 0.370452 0.185226 0.982696i \(-0.440698\pi\)
0.185226 + 0.982696i \(0.440698\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0.832022 0.0554681
\(226\) 12.7648 0.849105
\(227\) 20.4532 1.35753 0.678763 0.734357i \(-0.262516\pi\)
0.678763 + 0.734357i \(0.262516\pi\)
\(228\) −2.73858 −0.181367
\(229\) −29.0317 −1.91847 −0.959234 0.282612i \(-0.908799\pi\)
−0.959234 + 0.282612i \(0.908799\pi\)
\(230\) 15.8907 1.04780
\(231\) 3.24698 0.213636
\(232\) 6.22322 0.408575
\(233\) 12.4742 0.817211 0.408605 0.912711i \(-0.366015\pi\)
0.408605 + 0.912711i \(0.366015\pi\)
\(234\) 0 0
\(235\) −23.6011 −1.53957
\(236\) −4.50007 −0.292930
\(237\) −2.41753 −0.157035
\(238\) 1.80194 0.116802
\(239\) −23.3225 −1.50861 −0.754303 0.656527i \(-0.772025\pi\)
−0.754303 + 0.656527i \(0.772025\pi\)
\(240\) −2.41496 −0.155885
\(241\) 28.8105 1.85584 0.927922 0.372773i \(-0.121593\pi\)
0.927922 + 0.372773i \(0.121593\pi\)
\(242\) −0.457123 −0.0293850
\(243\) 1.00000 0.0641500
\(244\) 6.94297 0.444478
\(245\) −2.41496 −0.154286
\(246\) 9.15862 0.583932
\(247\) 0 0
\(248\) 2.72294 0.172907
\(249\) −3.51468 −0.222734
\(250\) 10.0655 0.636598
\(251\) 1.56870 0.0990152 0.0495076 0.998774i \(-0.484235\pi\)
0.0495076 + 0.998774i \(0.484235\pi\)
\(252\) 1.00000 0.0629941
\(253\) −21.3655 −1.34324
\(254\) −11.7970 −0.740211
\(255\) −4.35160 −0.272508
\(256\) 1.00000 0.0625000
\(257\) −14.0911 −0.878981 −0.439491 0.898247i \(-0.644841\pi\)
−0.439491 + 0.898247i \(0.644841\pi\)
\(258\) −3.95322 −0.246117
\(259\) 8.93878 0.555429
\(260\) 0 0
\(261\) 6.22322 0.385208
\(262\) −16.5193 −1.02057
\(263\) −6.63837 −0.409339 −0.204670 0.978831i \(-0.565612\pi\)
−0.204670 + 0.978831i \(0.565612\pi\)
\(264\) 3.24698 0.199838
\(265\) 25.0544 1.53908
\(266\) −2.73858 −0.167913
\(267\) 10.9361 0.669276
\(268\) −2.54486 −0.155452
\(269\) 18.0426 1.10007 0.550037 0.835140i \(-0.314614\pi\)
0.550037 + 0.835140i \(0.314614\pi\)
\(270\) −2.41496 −0.146970
\(271\) 12.0877 0.734277 0.367139 0.930166i \(-0.380337\pi\)
0.367139 + 0.930166i \(0.380337\pi\)
\(272\) 1.80194 0.109259
\(273\) 0 0
\(274\) 11.5650 0.698670
\(275\) 2.70156 0.162910
\(276\) −6.58012 −0.396077
\(277\) 30.1936 1.81416 0.907080 0.420958i \(-0.138306\pi\)
0.907080 + 0.420958i \(0.138306\pi\)
\(278\) −2.63433 −0.157997
\(279\) 2.72294 0.163018
\(280\) −2.41496 −0.144321
\(281\) 20.4356 1.21909 0.609543 0.792753i \(-0.291353\pi\)
0.609543 + 0.792753i \(0.291353\pi\)
\(282\) 9.77289 0.581967
\(283\) −4.01876 −0.238890 −0.119445 0.992841i \(-0.538112\pi\)
−0.119445 + 0.992841i \(0.538112\pi\)
\(284\) −1.50961 −0.0895787
\(285\) 6.61356 0.391754
\(286\) 0 0
\(287\) 9.15862 0.540616
\(288\) 1.00000 0.0589256
\(289\) −13.7530 −0.809001
\(290\) −15.0288 −0.882523
\(291\) 12.2904 0.720475
\(292\) −0.786291 −0.0460142
\(293\) 19.3490 1.13038 0.565191 0.824960i \(-0.308802\pi\)
0.565191 + 0.824960i \(0.308802\pi\)
\(294\) 1.00000 0.0583212
\(295\) 10.8675 0.632729
\(296\) 8.93878 0.519556
\(297\) 3.24698 0.188409
\(298\) −19.3553 −1.12122
\(299\) 0 0
\(300\) 0.832022 0.0480368
\(301\) −3.95322 −0.227860
\(302\) 9.50760 0.547101
\(303\) 15.5746 0.894738
\(304\) −2.73858 −0.157069
\(305\) −16.7670 −0.960075
\(306\) 1.80194 0.103010
\(307\) 5.04050 0.287677 0.143838 0.989601i \(-0.454055\pi\)
0.143838 + 0.989601i \(0.454055\pi\)
\(308\) 3.24698 0.185014
\(309\) 3.71813 0.211517
\(310\) −6.57578 −0.373479
\(311\) −16.2638 −0.922235 −0.461117 0.887339i \(-0.652551\pi\)
−0.461117 + 0.887339i \(0.652551\pi\)
\(312\) 0 0
\(313\) −8.80560 −0.497722 −0.248861 0.968539i \(-0.580056\pi\)
−0.248861 + 0.968539i \(0.580056\pi\)
\(314\) 2.70530 0.152669
\(315\) −2.41496 −0.136067
\(316\) −2.41753 −0.135997
\(317\) 20.0495 1.12609 0.563047 0.826425i \(-0.309629\pi\)
0.563047 + 0.826425i \(0.309629\pi\)
\(318\) −10.3747 −0.581783
\(319\) 20.2067 1.13136
\(320\) −2.41496 −0.135000
\(321\) −0.125781 −0.00702039
\(322\) −6.58012 −0.366696
\(323\) −4.93476 −0.274577
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −6.79361 −0.376263
\(327\) 3.84276 0.212505
\(328\) 9.15862 0.505700
\(329\) 9.77289 0.538797
\(330\) −7.84132 −0.431650
\(331\) −19.0732 −1.04836 −0.524180 0.851607i \(-0.675628\pi\)
−0.524180 + 0.851607i \(0.675628\pi\)
\(332\) −3.51468 −0.192893
\(333\) 8.93878 0.489842
\(334\) 17.9654 0.983021
\(335\) 6.14573 0.335777
\(336\) 1.00000 0.0545545
\(337\) 14.8542 0.809159 0.404580 0.914503i \(-0.367418\pi\)
0.404580 + 0.914503i \(0.367418\pi\)
\(338\) 0 0
\(339\) 12.7648 0.693291
\(340\) −4.35160 −0.235999
\(341\) 8.84132 0.478784
\(342\) −2.73858 −0.148086
\(343\) 1.00000 0.0539949
\(344\) −3.95322 −0.213143
\(345\) 15.8907 0.855527
\(346\) −7.21332 −0.387790
\(347\) 26.6896 1.43277 0.716386 0.697704i \(-0.245795\pi\)
0.716386 + 0.697704i \(0.245795\pi\)
\(348\) 6.22322 0.333600
\(349\) −31.8560 −1.70521 −0.852607 0.522552i \(-0.824980\pi\)
−0.852607 + 0.522552i \(0.824980\pi\)
\(350\) 0.832022 0.0444734
\(351\) 0 0
\(352\) 3.24698 0.173065
\(353\) −3.52242 −0.187480 −0.0937398 0.995597i \(-0.529882\pi\)
−0.0937398 + 0.995597i \(0.529882\pi\)
\(354\) −4.50007 −0.239176
\(355\) 3.64564 0.193490
\(356\) 10.9361 0.579610
\(357\) 1.80194 0.0953687
\(358\) 3.27893 0.173297
\(359\) 24.0153 1.26748 0.633740 0.773546i \(-0.281519\pi\)
0.633740 + 0.773546i \(0.281519\pi\)
\(360\) −2.41496 −0.127279
\(361\) −11.5002 −0.605272
\(362\) 21.0091 1.10422
\(363\) −0.457123 −0.0239928
\(364\) 0 0
\(365\) 1.89886 0.0993908
\(366\) 6.94297 0.362915
\(367\) −5.01103 −0.261574 −0.130787 0.991411i \(-0.541750\pi\)
−0.130787 + 0.991411i \(0.541750\pi\)
\(368\) −6.58012 −0.343012
\(369\) 9.15862 0.476779
\(370\) −21.5868 −1.12224
\(371\) −10.3747 −0.538627
\(372\) 2.72294 0.141178
\(373\) −12.2463 −0.634092 −0.317046 0.948410i \(-0.602691\pi\)
−0.317046 + 0.948410i \(0.602691\pi\)
\(374\) 5.85086 0.302541
\(375\) 10.0655 0.519780
\(376\) 9.77289 0.503998
\(377\) 0 0
\(378\) 1.00000 0.0514344
\(379\) −15.3669 −0.789343 −0.394672 0.918822i \(-0.629142\pi\)
−0.394672 + 0.918822i \(0.629142\pi\)
\(380\) 6.61356 0.339269
\(381\) −11.7970 −0.604379
\(382\) −6.15290 −0.314810
\(383\) 13.7125 0.700675 0.350338 0.936623i \(-0.386067\pi\)
0.350338 + 0.936623i \(0.386067\pi\)
\(384\) 1.00000 0.0510310
\(385\) −7.84132 −0.399631
\(386\) −18.6232 −0.947897
\(387\) −3.95322 −0.200954
\(388\) 12.2904 0.623950
\(389\) 9.05551 0.459133 0.229566 0.973293i \(-0.426269\pi\)
0.229566 + 0.973293i \(0.426269\pi\)
\(390\) 0 0
\(391\) −11.8570 −0.599633
\(392\) 1.00000 0.0505076
\(393\) −16.5193 −0.833288
\(394\) 16.8553 0.849155
\(395\) 5.83823 0.293753
\(396\) 3.24698 0.163167
\(397\) −20.8502 −1.04644 −0.523220 0.852198i \(-0.675269\pi\)
−0.523220 + 0.852198i \(0.675269\pi\)
\(398\) 12.3376 0.618428
\(399\) −2.73858 −0.137101
\(400\) 0.832022 0.0416011
\(401\) −19.6443 −0.980988 −0.490494 0.871445i \(-0.663184\pi\)
−0.490494 + 0.871445i \(0.663184\pi\)
\(402\) −2.54486 −0.126926
\(403\) 0 0
\(404\) 15.5746 0.774866
\(405\) −2.41496 −0.120000
\(406\) 6.22322 0.308853
\(407\) 29.0240 1.43867
\(408\) 1.80194 0.0892092
\(409\) −2.96748 −0.146733 −0.0733663 0.997305i \(-0.523374\pi\)
−0.0733663 + 0.997305i \(0.523374\pi\)
\(410\) −22.1177 −1.09231
\(411\) 11.5650 0.570461
\(412\) 3.71813 0.183179
\(413\) −4.50007 −0.221434
\(414\) −6.58012 −0.323395
\(415\) 8.48781 0.416650
\(416\) 0 0
\(417\) −2.63433 −0.129004
\(418\) −8.89213 −0.434928
\(419\) −0.255356 −0.0124750 −0.00623748 0.999981i \(-0.501985\pi\)
−0.00623748 + 0.999981i \(0.501985\pi\)
\(420\) −2.41496 −0.117838
\(421\) −36.2298 −1.76573 −0.882867 0.469623i \(-0.844390\pi\)
−0.882867 + 0.469623i \(0.844390\pi\)
\(422\) −15.6160 −0.760176
\(423\) 9.77289 0.475174
\(424\) −10.3747 −0.503839
\(425\) 1.49925 0.0727244
\(426\) −1.50961 −0.0731407
\(427\) 6.94297 0.335994
\(428\) −0.125781 −0.00607983
\(429\) 0 0
\(430\) 9.54686 0.460391
\(431\) 26.6462 1.28350 0.641752 0.766913i \(-0.278208\pi\)
0.641752 + 0.766913i \(0.278208\pi\)
\(432\) 1.00000 0.0481125
\(433\) −30.6061 −1.47083 −0.735417 0.677615i \(-0.763014\pi\)
−0.735417 + 0.677615i \(0.763014\pi\)
\(434\) 2.72294 0.130705
\(435\) −15.0288 −0.720577
\(436\) 3.84276 0.184035
\(437\) 18.0202 0.862023
\(438\) −0.786291 −0.0375704
\(439\) −11.4091 −0.544525 −0.272262 0.962223i \(-0.587772\pi\)
−0.272262 + 0.962223i \(0.587772\pi\)
\(440\) −7.84132 −0.373820
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) 38.5387 1.83103 0.915515 0.402283i \(-0.131783\pi\)
0.915515 + 0.402283i \(0.131783\pi\)
\(444\) 8.93878 0.424216
\(445\) −26.4101 −1.25196
\(446\) 5.53203 0.261949
\(447\) −19.3553 −0.915475
\(448\) 1.00000 0.0472456
\(449\) −2.16519 −0.102182 −0.0510908 0.998694i \(-0.516270\pi\)
−0.0510908 + 0.998694i \(0.516270\pi\)
\(450\) 0.832022 0.0392219
\(451\) 29.7378 1.40030
\(452\) 12.7648 0.600408
\(453\) 9.50760 0.446706
\(454\) 20.4532 0.959917
\(455\) 0 0
\(456\) −2.73858 −0.128246
\(457\) −31.4845 −1.47278 −0.736392 0.676555i \(-0.763472\pi\)
−0.736392 + 0.676555i \(0.763472\pi\)
\(458\) −29.0317 −1.35656
\(459\) 1.80194 0.0841073
\(460\) 15.8907 0.740908
\(461\) 7.94726 0.370141 0.185070 0.982725i \(-0.440749\pi\)
0.185070 + 0.982725i \(0.440749\pi\)
\(462\) 3.24698 0.151063
\(463\) 12.1131 0.562943 0.281471 0.959570i \(-0.409178\pi\)
0.281471 + 0.959570i \(0.409178\pi\)
\(464\) 6.22322 0.288906
\(465\) −6.57578 −0.304944
\(466\) 12.4742 0.577855
\(467\) −1.69520 −0.0784446 −0.0392223 0.999231i \(-0.512488\pi\)
−0.0392223 + 0.999231i \(0.512488\pi\)
\(468\) 0 0
\(469\) −2.54486 −0.117511
\(470\) −23.6011 −1.08864
\(471\) 2.70530 0.124654
\(472\) −4.50007 −0.207133
\(473\) −12.8360 −0.590201
\(474\) −2.41753 −0.111041
\(475\) −2.27856 −0.104548
\(476\) 1.80194 0.0825917
\(477\) −10.3747 −0.475024
\(478\) −23.3225 −1.06675
\(479\) 3.59340 0.164187 0.0820933 0.996625i \(-0.473839\pi\)
0.0820933 + 0.996625i \(0.473839\pi\)
\(480\) −2.41496 −0.110227
\(481\) 0 0
\(482\) 28.8105 1.31228
\(483\) −6.58012 −0.299406
\(484\) −0.457123 −0.0207783
\(485\) −29.6808 −1.34773
\(486\) 1.00000 0.0453609
\(487\) −4.79109 −0.217105 −0.108552 0.994091i \(-0.534622\pi\)
−0.108552 + 0.994091i \(0.534622\pi\)
\(488\) 6.94297 0.314294
\(489\) −6.79361 −0.307218
\(490\) −2.41496 −0.109097
\(491\) −42.3139 −1.90960 −0.954800 0.297250i \(-0.903931\pi\)
−0.954800 + 0.297250i \(0.903931\pi\)
\(492\) 9.15862 0.412902
\(493\) 11.2139 0.505047
\(494\) 0 0
\(495\) −7.84132 −0.352441
\(496\) 2.72294 0.122263
\(497\) −1.50961 −0.0677151
\(498\) −3.51468 −0.157497
\(499\) 26.4820 1.18550 0.592749 0.805387i \(-0.298042\pi\)
0.592749 + 0.805387i \(0.298042\pi\)
\(500\) 10.0655 0.450142
\(501\) 17.9654 0.802633
\(502\) 1.56870 0.0700143
\(503\) 16.9580 0.756121 0.378060 0.925781i \(-0.376591\pi\)
0.378060 + 0.925781i \(0.376591\pi\)
\(504\) 1.00000 0.0445435
\(505\) −37.6120 −1.67371
\(506\) −21.3655 −0.949813
\(507\) 0 0
\(508\) −11.7970 −0.523408
\(509\) −3.29901 −0.146226 −0.0731129 0.997324i \(-0.523293\pi\)
−0.0731129 + 0.997324i \(0.523293\pi\)
\(510\) −4.35160 −0.192692
\(511\) −0.786291 −0.0347834
\(512\) 1.00000 0.0441942
\(513\) −2.73858 −0.120911
\(514\) −14.0911 −0.621534
\(515\) −8.97913 −0.395668
\(516\) −3.95322 −0.174031
\(517\) 31.7324 1.39559
\(518\) 8.93878 0.392748
\(519\) −7.21332 −0.316630
\(520\) 0 0
\(521\) −3.85188 −0.168754 −0.0843770 0.996434i \(-0.526890\pi\)
−0.0843770 + 0.996434i \(0.526890\pi\)
\(522\) 6.22322 0.272383
\(523\) −13.8862 −0.607201 −0.303601 0.952799i \(-0.598189\pi\)
−0.303601 + 0.952799i \(0.598189\pi\)
\(524\) −16.5193 −0.721649
\(525\) 0.832022 0.0363124
\(526\) −6.63837 −0.289447
\(527\) 4.90656 0.213733
\(528\) 3.24698 0.141307
\(529\) 20.2980 0.882521
\(530\) 25.0544 1.08829
\(531\) −4.50007 −0.195286
\(532\) −2.73858 −0.118733
\(533\) 0 0
\(534\) 10.9361 0.473250
\(535\) 0.303755 0.0131325
\(536\) −2.54486 −0.109921
\(537\) 3.27893 0.141496
\(538\) 18.0426 0.777870
\(539\) 3.24698 0.139857
\(540\) −2.41496 −0.103923
\(541\) 5.36925 0.230842 0.115421 0.993317i \(-0.463178\pi\)
0.115421 + 0.993317i \(0.463178\pi\)
\(542\) 12.0877 0.519212
\(543\) 21.0091 0.901588
\(544\) 1.80194 0.0772574
\(545\) −9.28010 −0.397516
\(546\) 0 0
\(547\) −46.0980 −1.97101 −0.985504 0.169653i \(-0.945735\pi\)
−0.985504 + 0.169653i \(0.945735\pi\)
\(548\) 11.5650 0.494034
\(549\) 6.94297 0.296319
\(550\) 2.70156 0.115195
\(551\) −17.0428 −0.726049
\(552\) −6.58012 −0.280068
\(553\) −2.41753 −0.102804
\(554\) 30.1936 1.28281
\(555\) −21.5868 −0.916308
\(556\) −2.63433 −0.111720
\(557\) 15.3154 0.648936 0.324468 0.945897i \(-0.394815\pi\)
0.324468 + 0.945897i \(0.394815\pi\)
\(558\) 2.72294 0.115271
\(559\) 0 0
\(560\) −2.41496 −0.102051
\(561\) 5.85086 0.247023
\(562\) 20.4356 0.862023
\(563\) −8.13781 −0.342968 −0.171484 0.985187i \(-0.554856\pi\)
−0.171484 + 0.985187i \(0.554856\pi\)
\(564\) 9.77289 0.411513
\(565\) −30.8266 −1.29688
\(566\) −4.01876 −0.168921
\(567\) 1.00000 0.0419961
\(568\) −1.50961 −0.0633417
\(569\) −15.9128 −0.667099 −0.333550 0.942733i \(-0.608246\pi\)
−0.333550 + 0.942733i \(0.608246\pi\)
\(570\) 6.61356 0.277012
\(571\) 29.3918 1.23001 0.615004 0.788524i \(-0.289154\pi\)
0.615004 + 0.788524i \(0.289154\pi\)
\(572\) 0 0
\(573\) −6.15290 −0.257041
\(574\) 9.15862 0.382273
\(575\) −5.47480 −0.228315
\(576\) 1.00000 0.0416667
\(577\) −22.0602 −0.918377 −0.459188 0.888339i \(-0.651860\pi\)
−0.459188 + 0.888339i \(0.651860\pi\)
\(578\) −13.7530 −0.572050
\(579\) −18.6232 −0.773955
\(580\) −15.0288 −0.624038
\(581\) −3.51468 −0.145814
\(582\) 12.2904 0.509453
\(583\) −33.6864 −1.39515
\(584\) −0.786291 −0.0325369
\(585\) 0 0
\(586\) 19.3490 0.799301
\(587\) 42.3330 1.74727 0.873634 0.486583i \(-0.161757\pi\)
0.873634 + 0.486583i \(0.161757\pi\)
\(588\) 1.00000 0.0412393
\(589\) −7.45699 −0.307260
\(590\) 10.8675 0.447407
\(591\) 16.8553 0.693332
\(592\) 8.93878 0.367382
\(593\) −13.0257 −0.534903 −0.267451 0.963571i \(-0.586182\pi\)
−0.267451 + 0.963571i \(0.586182\pi\)
\(594\) 3.24698 0.133225
\(595\) −4.35160 −0.178398
\(596\) −19.3553 −0.792825
\(597\) 12.3376 0.504944
\(598\) 0 0
\(599\) −28.1604 −1.15060 −0.575301 0.817941i \(-0.695115\pi\)
−0.575301 + 0.817941i \(0.695115\pi\)
\(600\) 0.832022 0.0339671
\(601\) 26.9245 1.09827 0.549136 0.835733i \(-0.314957\pi\)
0.549136 + 0.835733i \(0.314957\pi\)
\(602\) −3.95322 −0.161121
\(603\) −2.54486 −0.103635
\(604\) 9.50760 0.386859
\(605\) 1.10393 0.0448813
\(606\) 15.5746 0.632675
\(607\) 19.1584 0.777617 0.388808 0.921319i \(-0.372887\pi\)
0.388808 + 0.921319i \(0.372887\pi\)
\(608\) −2.73858 −0.111064
\(609\) 6.22322 0.252178
\(610\) −16.7670 −0.678876
\(611\) 0 0
\(612\) 1.80194 0.0728390
\(613\) −3.78753 −0.152977 −0.0764884 0.997070i \(-0.524371\pi\)
−0.0764884 + 0.997070i \(0.524371\pi\)
\(614\) 5.04050 0.203418
\(615\) −22.1177 −0.891871
\(616\) 3.24698 0.130825
\(617\) −24.0329 −0.967527 −0.483764 0.875199i \(-0.660731\pi\)
−0.483764 + 0.875199i \(0.660731\pi\)
\(618\) 3.71813 0.149565
\(619\) −44.5020 −1.78869 −0.894344 0.447381i \(-0.852357\pi\)
−0.894344 + 0.447381i \(0.852357\pi\)
\(620\) −6.57578 −0.264090
\(621\) −6.58012 −0.264051
\(622\) −16.2638 −0.652118
\(623\) 10.9361 0.438144
\(624\) 0 0
\(625\) −28.4678 −1.13871
\(626\) −8.80560 −0.351943
\(627\) −8.89213 −0.355117
\(628\) 2.70530 0.107953
\(629\) 16.1071 0.642233
\(630\) −2.41496 −0.0962142
\(631\) −26.0186 −1.03579 −0.517893 0.855446i \(-0.673283\pi\)
−0.517893 + 0.855446i \(0.673283\pi\)
\(632\) −2.41753 −0.0961642
\(633\) −15.6160 −0.620681
\(634\) 20.0495 0.796269
\(635\) 28.4893 1.13056
\(636\) −10.3747 −0.411383
\(637\) 0 0
\(638\) 20.2067 0.799990
\(639\) −1.50961 −0.0597191
\(640\) −2.41496 −0.0954596
\(641\) −37.8504 −1.49500 −0.747500 0.664261i \(-0.768746\pi\)
−0.747500 + 0.664261i \(0.768746\pi\)
\(642\) −0.125781 −0.00496416
\(643\) 26.4910 1.04470 0.522351 0.852731i \(-0.325055\pi\)
0.522351 + 0.852731i \(0.325055\pi\)
\(644\) −6.58012 −0.259293
\(645\) 9.54686 0.375907
\(646\) −4.93476 −0.194155
\(647\) −34.8792 −1.37124 −0.685621 0.727959i \(-0.740469\pi\)
−0.685621 + 0.727959i \(0.740469\pi\)
\(648\) 1.00000 0.0392837
\(649\) −14.6116 −0.573557
\(650\) 0 0
\(651\) 2.72294 0.106720
\(652\) −6.79361 −0.266058
\(653\) 0.351211 0.0137439 0.00687197 0.999976i \(-0.497813\pi\)
0.00687197 + 0.999976i \(0.497813\pi\)
\(654\) 3.84276 0.150264
\(655\) 39.8934 1.55876
\(656\) 9.15862 0.357584
\(657\) −0.786291 −0.0306761
\(658\) 9.77289 0.380987
\(659\) 10.6161 0.413545 0.206773 0.978389i \(-0.433704\pi\)
0.206773 + 0.978389i \(0.433704\pi\)
\(660\) −7.84132 −0.305223
\(661\) −45.2269 −1.75912 −0.879561 0.475786i \(-0.842164\pi\)
−0.879561 + 0.475786i \(0.842164\pi\)
\(662\) −19.0732 −0.741303
\(663\) 0 0
\(664\) −3.51468 −0.136396
\(665\) 6.61356 0.256463
\(666\) 8.93878 0.346371
\(667\) −40.9496 −1.58557
\(668\) 17.9654 0.695101
\(669\) 5.53203 0.213881
\(670\) 6.14573 0.237430
\(671\) 22.5437 0.870290
\(672\) 1.00000 0.0385758
\(673\) 16.2910 0.627973 0.313986 0.949428i \(-0.398335\pi\)
0.313986 + 0.949428i \(0.398335\pi\)
\(674\) 14.8542 0.572162
\(675\) 0.832022 0.0320245
\(676\) 0 0
\(677\) −29.8672 −1.14789 −0.573946 0.818893i \(-0.694588\pi\)
−0.573946 + 0.818893i \(0.694588\pi\)
\(678\) 12.7648 0.490231
\(679\) 12.2904 0.471662
\(680\) −4.35160 −0.166876
\(681\) 20.4532 0.783769
\(682\) 8.84132 0.338552
\(683\) −3.26490 −0.124928 −0.0624640 0.998047i \(-0.519896\pi\)
−0.0624640 + 0.998047i \(0.519896\pi\)
\(684\) −2.73858 −0.104712
\(685\) −27.9291 −1.06712
\(686\) 1.00000 0.0381802
\(687\) −29.0317 −1.10763
\(688\) −3.95322 −0.150715
\(689\) 0 0
\(690\) 15.8907 0.604949
\(691\) 38.2216 1.45402 0.727010 0.686627i \(-0.240910\pi\)
0.727010 + 0.686627i \(0.240910\pi\)
\(692\) −7.21332 −0.274209
\(693\) 3.24698 0.123343
\(694\) 26.6896 1.01312
\(695\) 6.36179 0.241317
\(696\) 6.22322 0.235891
\(697\) 16.5033 0.625105
\(698\) −31.8560 −1.20577
\(699\) 12.4742 0.471817
\(700\) 0.832022 0.0314475
\(701\) −16.1383 −0.609535 −0.304767 0.952427i \(-0.598579\pi\)
−0.304767 + 0.952427i \(0.598579\pi\)
\(702\) 0 0
\(703\) −24.4796 −0.923266
\(704\) 3.24698 0.122375
\(705\) −23.6011 −0.888870
\(706\) −3.52242 −0.132568
\(707\) 15.5746 0.585744
\(708\) −4.50007 −0.169123
\(709\) 17.2856 0.649176 0.324588 0.945856i \(-0.394774\pi\)
0.324588 + 0.945856i \(0.394774\pi\)
\(710\) 3.64564 0.136818
\(711\) −2.41753 −0.0906645
\(712\) 10.9361 0.409846
\(713\) −17.9172 −0.671006
\(714\) 1.80194 0.0674358
\(715\) 0 0
\(716\) 3.27893 0.122539
\(717\) −23.3225 −0.870994
\(718\) 24.0153 0.896244
\(719\) −32.0469 −1.19515 −0.597574 0.801814i \(-0.703868\pi\)
−0.597574 + 0.801814i \(0.703868\pi\)
\(720\) −2.41496 −0.0900002
\(721\) 3.71813 0.138470
\(722\) −11.5002 −0.427992
\(723\) 28.8105 1.07147
\(724\) 21.0091 0.780798
\(725\) 5.17786 0.192301
\(726\) −0.457123 −0.0169654
\(727\) −9.14186 −0.339053 −0.169526 0.985526i \(-0.554224\pi\)
−0.169526 + 0.985526i \(0.554224\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 1.89886 0.0702799
\(731\) −7.12346 −0.263471
\(732\) 6.94297 0.256620
\(733\) −0.298008 −0.0110072 −0.00550359 0.999985i \(-0.501752\pi\)
−0.00550359 + 0.999985i \(0.501752\pi\)
\(734\) −5.01103 −0.184961
\(735\) −2.41496 −0.0890771
\(736\) −6.58012 −0.242546
\(737\) −8.26311 −0.304376
\(738\) 9.15862 0.337133
\(739\) −20.7127 −0.761931 −0.380965 0.924589i \(-0.624408\pi\)
−0.380965 + 0.924589i \(0.624408\pi\)
\(740\) −21.5868 −0.793546
\(741\) 0 0
\(742\) −10.3747 −0.380867
\(743\) −43.7005 −1.60322 −0.801608 0.597849i \(-0.796022\pi\)
−0.801608 + 0.597849i \(0.796022\pi\)
\(744\) 2.72294 0.0998277
\(745\) 46.7423 1.71250
\(746\) −12.2463 −0.448371
\(747\) −3.51468 −0.128595
\(748\) 5.85086 0.213928
\(749\) −0.125781 −0.00459592
\(750\) 10.0655 0.367540
\(751\) −51.8962 −1.89372 −0.946860 0.321646i \(-0.895764\pi\)
−0.946860 + 0.321646i \(0.895764\pi\)
\(752\) 9.77289 0.356381
\(753\) 1.56870 0.0571664
\(754\) 0 0
\(755\) −22.9604 −0.835616
\(756\) 1.00000 0.0363696
\(757\) 47.3170 1.71977 0.859883 0.510491i \(-0.170536\pi\)
0.859883 + 0.510491i \(0.170536\pi\)
\(758\) −15.3669 −0.558150
\(759\) −21.3655 −0.775519
\(760\) 6.61356 0.239899
\(761\) 13.5638 0.491687 0.245844 0.969310i \(-0.420935\pi\)
0.245844 + 0.969310i \(0.420935\pi\)
\(762\) −11.7970 −0.427361
\(763\) 3.84276 0.139117
\(764\) −6.15290 −0.222604
\(765\) −4.35160 −0.157333
\(766\) 13.7125 0.495452
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) −32.6689 −1.17807 −0.589036 0.808107i \(-0.700492\pi\)
−0.589036 + 0.808107i \(0.700492\pi\)
\(770\) −7.84132 −0.282582
\(771\) −14.0911 −0.507480
\(772\) −18.6232 −0.670265
\(773\) 31.1438 1.12016 0.560082 0.828437i \(-0.310770\pi\)
0.560082 + 0.828437i \(0.310770\pi\)
\(774\) −3.95322 −0.142096
\(775\) 2.26554 0.0813807
\(776\) 12.2904 0.441199
\(777\) 8.93878 0.320677
\(778\) 9.05551 0.324656
\(779\) −25.0816 −0.898643
\(780\) 0 0
\(781\) −4.90166 −0.175395
\(782\) −11.8570 −0.424004
\(783\) 6.22322 0.222400
\(784\) 1.00000 0.0357143
\(785\) −6.53320 −0.233180
\(786\) −16.5193 −0.589224
\(787\) −32.0019 −1.14075 −0.570373 0.821386i \(-0.693201\pi\)
−0.570373 + 0.821386i \(0.693201\pi\)
\(788\) 16.8553 0.600443
\(789\) −6.63837 −0.236332
\(790\) 5.83823 0.207715
\(791\) 12.7648 0.453866
\(792\) 3.24698 0.115376
\(793\) 0 0
\(794\) −20.8502 −0.739944
\(795\) 25.0544 0.888589
\(796\) 12.3376 0.437295
\(797\) −23.5034 −0.832532 −0.416266 0.909243i \(-0.636661\pi\)
−0.416266 + 0.909243i \(0.636661\pi\)
\(798\) −2.73858 −0.0969448
\(799\) 17.6101 0.623002
\(800\) 0.832022 0.0294164
\(801\) 10.9361 0.386407
\(802\) −19.6443 −0.693663
\(803\) −2.55307 −0.0900959
\(804\) −2.54486 −0.0897504
\(805\) 15.8907 0.560074
\(806\) 0 0
\(807\) 18.0426 0.635128
\(808\) 15.5746 0.547913
\(809\) 0.626708 0.0220339 0.0110169 0.999939i \(-0.496493\pi\)
0.0110169 + 0.999939i \(0.496493\pi\)
\(810\) −2.41496 −0.0848530
\(811\) −2.31714 −0.0813656 −0.0406828 0.999172i \(-0.512953\pi\)
−0.0406828 + 0.999172i \(0.512953\pi\)
\(812\) 6.22322 0.218392
\(813\) 12.0877 0.423935
\(814\) 29.0240 1.01729
\(815\) 16.4063 0.574687
\(816\) 1.80194 0.0630804
\(817\) 10.8262 0.378762
\(818\) −2.96748 −0.103756
\(819\) 0 0
\(820\) −22.1177 −0.772383
\(821\) 45.6066 1.59168 0.795841 0.605505i \(-0.207029\pi\)
0.795841 + 0.605505i \(0.207029\pi\)
\(822\) 11.5650 0.403377
\(823\) 54.7826 1.90960 0.954801 0.297246i \(-0.0960680\pi\)
0.954801 + 0.297246i \(0.0960680\pi\)
\(824\) 3.71813 0.129527
\(825\) 2.70156 0.0940562
\(826\) −4.50007 −0.156577
\(827\) 5.65372 0.196599 0.0982995 0.995157i \(-0.468660\pi\)
0.0982995 + 0.995157i \(0.468660\pi\)
\(828\) −6.58012 −0.228675
\(829\) −8.87143 −0.308117 −0.154059 0.988062i \(-0.549235\pi\)
−0.154059 + 0.988062i \(0.549235\pi\)
\(830\) 8.48781 0.294616
\(831\) 30.1936 1.04741
\(832\) 0 0
\(833\) 1.80194 0.0624334
\(834\) −2.63433 −0.0912194
\(835\) −43.3856 −1.50142
\(836\) −8.89213 −0.307541
\(837\) 2.72294 0.0941185
\(838\) −0.255356 −0.00882112
\(839\) 1.78656 0.0616789 0.0308394 0.999524i \(-0.490182\pi\)
0.0308394 + 0.999524i \(0.490182\pi\)
\(840\) −2.41496 −0.0833240
\(841\) 9.72852 0.335466
\(842\) −36.2298 −1.24856
\(843\) 20.4356 0.703839
\(844\) −15.6160 −0.537525
\(845\) 0 0
\(846\) 9.77289 0.335999
\(847\) −0.457123 −0.0157069
\(848\) −10.3747 −0.356268
\(849\) −4.01876 −0.137923
\(850\) 1.49925 0.0514239
\(851\) −58.8183 −2.01626
\(852\) −1.50961 −0.0517183
\(853\) −33.5043 −1.14716 −0.573582 0.819148i \(-0.694447\pi\)
−0.573582 + 0.819148i \(0.694447\pi\)
\(854\) 6.94297 0.237584
\(855\) 6.61356 0.226179
\(856\) −0.125781 −0.00429909
\(857\) −1.66717 −0.0569496 −0.0284748 0.999595i \(-0.509065\pi\)
−0.0284748 + 0.999595i \(0.509065\pi\)
\(858\) 0 0
\(859\) 2.42584 0.0827685 0.0413842 0.999143i \(-0.486823\pi\)
0.0413842 + 0.999143i \(0.486823\pi\)
\(860\) 9.54686 0.325545
\(861\) 9.15862 0.312125
\(862\) 26.6462 0.907574
\(863\) −25.5617 −0.870132 −0.435066 0.900399i \(-0.643275\pi\)
−0.435066 + 0.900399i \(0.643275\pi\)
\(864\) 1.00000 0.0340207
\(865\) 17.4199 0.592293
\(866\) −30.6061 −1.04004
\(867\) −13.7530 −0.467077
\(868\) 2.72294 0.0924225
\(869\) −7.84967 −0.266282
\(870\) −15.0288 −0.509525
\(871\) 0 0
\(872\) 3.84276 0.130132
\(873\) 12.2904 0.415967
\(874\) 18.0202 0.609543
\(875\) 10.0655 0.340276
\(876\) −0.786291 −0.0265663
\(877\) −5.50129 −0.185765 −0.0928827 0.995677i \(-0.529608\pi\)
−0.0928827 + 0.995677i \(0.529608\pi\)
\(878\) −11.4091 −0.385037
\(879\) 19.3490 0.652627
\(880\) −7.84132 −0.264331
\(881\) −54.5279 −1.83709 −0.918546 0.395313i \(-0.870636\pi\)
−0.918546 + 0.395313i \(0.870636\pi\)
\(882\) 1.00000 0.0336718
\(883\) −29.0931 −0.979062 −0.489531 0.871986i \(-0.662832\pi\)
−0.489531 + 0.871986i \(0.662832\pi\)
\(884\) 0 0
\(885\) 10.8675 0.365306
\(886\) 38.5387 1.29473
\(887\) 0.0869906 0.00292086 0.00146043 0.999999i \(-0.499535\pi\)
0.00146043 + 0.999999i \(0.499535\pi\)
\(888\) 8.93878 0.299966
\(889\) −11.7970 −0.395659
\(890\) −26.4101 −0.885270
\(891\) 3.24698 0.108778
\(892\) 5.53203 0.185226
\(893\) −26.7639 −0.895619
\(894\) −19.3553 −0.647339
\(895\) −7.91848 −0.264686
\(896\) 1.00000 0.0334077
\(897\) 0 0
\(898\) −2.16519 −0.0722533
\(899\) 16.9454 0.565162
\(900\) 0.832022 0.0277341
\(901\) −18.6945 −0.622805
\(902\) 29.7378 0.990162
\(903\) −3.95322 −0.131555
\(904\) 12.7648 0.424552
\(905\) −50.7362 −1.68653
\(906\) 9.50760 0.315869
\(907\) 20.4983 0.680634 0.340317 0.940311i \(-0.389466\pi\)
0.340317 + 0.940311i \(0.389466\pi\)
\(908\) 20.4532 0.678763
\(909\) 15.5746 0.516577
\(910\) 0 0
\(911\) 31.1649 1.03254 0.516269 0.856426i \(-0.327320\pi\)
0.516269 + 0.856426i \(0.327320\pi\)
\(912\) −2.73858 −0.0906836
\(913\) −11.4121 −0.377685
\(914\) −31.4845 −1.04142
\(915\) −16.7670 −0.554300
\(916\) −29.0317 −0.959234
\(917\) −16.5193 −0.545515
\(918\) 1.80194 0.0594728
\(919\) −39.9574 −1.31807 −0.659037 0.752110i \(-0.729036\pi\)
−0.659037 + 0.752110i \(0.729036\pi\)
\(920\) 15.8907 0.523901
\(921\) 5.04050 0.166090
\(922\) 7.94726 0.261729
\(923\) 0 0
\(924\) 3.24698 0.106818
\(925\) 7.43726 0.244536
\(926\) 12.1131 0.398061
\(927\) 3.71813 0.122119
\(928\) 6.22322 0.204287
\(929\) 12.8743 0.422393 0.211196 0.977444i \(-0.432264\pi\)
0.211196 + 0.977444i \(0.432264\pi\)
\(930\) −6.57578 −0.215628
\(931\) −2.73858 −0.0897535
\(932\) 12.4742 0.408605
\(933\) −16.2638 −0.532452
\(934\) −1.69520 −0.0554687
\(935\) −14.1296 −0.462086
\(936\) 0 0
\(937\) −14.9053 −0.486936 −0.243468 0.969909i \(-0.578285\pi\)
−0.243468 + 0.969909i \(0.578285\pi\)
\(938\) −2.54486 −0.0830927
\(939\) −8.80560 −0.287360
\(940\) −23.6011 −0.769784
\(941\) −41.7852 −1.36216 −0.681080 0.732209i \(-0.738489\pi\)
−0.681080 + 0.732209i \(0.738489\pi\)
\(942\) 2.70530 0.0881436
\(943\) −60.2648 −1.96249
\(944\) −4.50007 −0.146465
\(945\) −2.41496 −0.0785586
\(946\) −12.8360 −0.417335
\(947\) −21.9153 −0.712151 −0.356076 0.934457i \(-0.615885\pi\)
−0.356076 + 0.934457i \(0.615885\pi\)
\(948\) −2.41753 −0.0785177
\(949\) 0 0
\(950\) −2.27856 −0.0739263
\(951\) 20.0495 0.650151
\(952\) 1.80194 0.0584011
\(953\) 31.7129 1.02728 0.513641 0.858005i \(-0.328296\pi\)
0.513641 + 0.858005i \(0.328296\pi\)
\(954\) −10.3747 −0.335893
\(955\) 14.8590 0.480826
\(956\) −23.3225 −0.754303
\(957\) 20.2067 0.653189
\(958\) 3.59340 0.116097
\(959\) 11.5650 0.373455
\(960\) −2.41496 −0.0779424
\(961\) −23.5856 −0.760826
\(962\) 0 0
\(963\) −0.125781 −0.00405322
\(964\) 28.8105 0.927922
\(965\) 44.9743 1.44777
\(966\) −6.58012 −0.211712
\(967\) 9.95706 0.320198 0.160099 0.987101i \(-0.448819\pi\)
0.160099 + 0.987101i \(0.448819\pi\)
\(968\) −0.457123 −0.0146925
\(969\) −4.93476 −0.158527
\(970\) −29.6808 −0.952992
\(971\) −7.29014 −0.233952 −0.116976 0.993135i \(-0.537320\pi\)
−0.116976 + 0.993135i \(0.537320\pi\)
\(972\) 1.00000 0.0320750
\(973\) −2.63433 −0.0844527
\(974\) −4.79109 −0.153516
\(975\) 0 0
\(976\) 6.94297 0.222239
\(977\) −15.2936 −0.489285 −0.244643 0.969613i \(-0.578671\pi\)
−0.244643 + 0.969613i \(0.578671\pi\)
\(978\) −6.79361 −0.217236
\(979\) 35.5092 1.13488
\(980\) −2.41496 −0.0771430
\(981\) 3.84276 0.122690
\(982\) −42.3139 −1.35029
\(983\) −53.3268 −1.70086 −0.850430 0.526089i \(-0.823658\pi\)
−0.850430 + 0.526089i \(0.823658\pi\)
\(984\) 9.15862 0.291966
\(985\) −40.7047 −1.29696
\(986\) 11.2139 0.357122
\(987\) 9.77289 0.311075
\(988\) 0 0
\(989\) 26.0127 0.827155
\(990\) −7.84132 −0.249213
\(991\) 31.4834 1.00010 0.500051 0.865996i \(-0.333314\pi\)
0.500051 + 0.865996i \(0.333314\pi\)
\(992\) 2.72294 0.0864533
\(993\) −19.0732 −0.605271
\(994\) −1.50961 −0.0478818
\(995\) −29.7948 −0.944558
\(996\) −3.51468 −0.111367
\(997\) −16.4135 −0.519819 −0.259910 0.965633i \(-0.583693\pi\)
−0.259910 + 0.965633i \(0.583693\pi\)
\(998\) 26.4820 0.838274
\(999\) 8.93878 0.282811
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 7098.2.a.ct.1.1 yes 6
13.12 even 2 7098.2.a.cr.1.6 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7098.2.a.cr.1.6 6 13.12 even 2
7098.2.a.ct.1.1 yes 6 1.1 even 1 trivial